The following Z-estimator lemma [1]} plays a key role in this consistency proof.
Let \(\Psi :\Theta \mapsto \mathbb {L}\)  and \(\Psi _n:\Theta \mapsto \mathbb {L}\)  be maps between two normed spaces, where \(\Theta \)  is a parameter space, \(\mathbb {L}\)  is some normed space, \(\Vert \cdot \Vert _\mathbb {L}\)  denotes the uniform norm,
\(\Psi \)  is a fixed map, and \(\Psi _n\)  is a data-dependent map.
